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单选题已知是方程的两个不同的解向量,则下列向量中,必是的对应于特征值的特征向量是

A.

B.

C.

D.

线性代数2023年秋季课程封面

学科：线性代数2023年秋季

时间：2023-11-13 11:38:46

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<img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">相似于<img src="https://tihai-oss-cloud.itihey.com/img/13b09077e2d89f614209c196966d107b.png">的充分条件是

A. <img src="https://tihai-oss-cloud.itihey.com/img/9950dc38643018a0b3890417b9fd3cd0.png">B. 秩( <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">)=秩( <img src="https://tihai-oss-cloud.itihey.com/img/13b09077e2d89f614209c196966d107b.png">)C. <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">与 <img src="https://tihai-oss-cloud.itihey.com/img/13b09077e2d89f614209c196966d107b.png">有相同的特征多项式D. <img src="https://tihai-oss-cloud.itihey.com/img/3c92995df84e0948e58ffa30c5590175.png">阶矩阵 <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">与 <img src="https://tihai-oss-cloud.itihey.com/img/13b09077e2d89f614209c196966d107b.png">有相同的特征值,且 <img src="https://tihai-oss-cloud.itihey.com/img/3c92995df84e0948e58ffa30c5590175.png">个特征值各不相同

已知三阶矩阵A的特征值为1,2,3,则行列式<img src="https://tihai-oss-cloud.itihey.com/img/af315ff34ceb72e90cd6c58818d550ed.png">

A. 0B. 1C. 6D. 36

设<img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">是<img src="https://tihai-oss-cloud.itihey.com/img/3c92995df84e0948e58ffa30c5590175.png">阶矩阵,若<img src="https://tihai-oss-cloud.itihey.com/img/3663e385465b2955f3514fd0c59b42ca.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">的特征值

A. 全是零B. 全不是零C. 至少有一个是零D. 可以是任意数

已知<img src="https://tihai-oss-cloud.itihey.com/img/bc3cea95bc2f44014925fb0951299f83.png">为<img src="https://tihai-oss-cloud.itihey.com/img/660e847f6399a552faa2424a0d1e5343.png">阶可逆矩阵,那么与<img src="https://tihai-oss-cloud.itihey.com/img/bc3cea95bc2f44014925fb0951299f83.png">有相同特征值的矩阵是

A. <img src="https://tihai-oss-cloud.itihey.com/img/0cd0284fd4e3004669b75cd611a0def8.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/81fa9eea45ddb8999080cf310748c61f.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/eb4f23c6620be63edff034b5e2d01d16.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/570aea27e0718f3a4a8d129aea80e1c7.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/620050585c162700d9ad70b32c1b8149.png">分别是2阶方阵<img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">的属于不同特征值<img src="https://tihai-oss-cloud.itihey.com/img/969903ebd373f25a5936b1104cc7d376.png">的特征向量,则下列结论正确的是

A. <img src="https://tihai-oss-cloud.itihey.com/img/c50d0690100dbe7da8d328485c6763ff.png">也是 <img src="https://tihai-oss-cloud.itihey.com/img/8e55491c3f93d10d4b2bb4658806d94a.png">的特征向量B. <img src="https://tihai-oss-cloud.itihey.com/img/c50d0690100dbe7da8d328485c6763ff.png">是 <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">的全部特征向量C. <img src="https://tihai-oss-cloud.itihey.com/img/c50d0690100dbe7da8d328485c6763ff.png">( <img src="https://tihai-oss-cloud.itihey.com/img/511a1a7a95c5a80969d378071ed09051.png">不全为零)是 <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">的全部特征向量D. <img src="https://tihai-oss-cloud.itihey.com/img/c50d0690100dbe7da8d328485c6763ff.png">( <img src="https://tihai-oss-cloud.itihey.com/img/511a1a7a95c5a80969d378071ed09051.png">均不为零)是 <img src="https://tihai-oss-cloud.itihey.com/img/777001e824cc769973342b8712a27636.png">的全部特征向量

已知3阶矩阵的3个特征值是<img src="https://tihai-oss-cloud.itihey.com/img/845776f225e1e2efb31966375827f157.png">,则下列矩阵中是可逆矩阵的是

A. <img src="https://tihai-oss-cloud.itihey.com/img/334021684324050e25acb5be2c7cb02c.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d99a0ad89be6cc29c781bc18e7382d85.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/99ec98699065e513938bb36143a51f1f.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/2b850357d5060439e1130d5f720fcf58.png">

已知<img src="https://tihai-oss-cloud.itihey.com/img/d058a47a9687658a08af00a3f66baa66.png">是方程<img src="https://tihai-oss-cloud.itihey.com/img/119d5558ffd70fd58d4956d1a40fe036.png">的两个不同的解向量,则下列向量中,必是<img src="https://tihai-oss-cloud.itihey.com/img/8e55491c3f93d10d4b2bb4658806d94a.png">的对应于特征值<img src="https://tihai-oss-cloud.itihey.com/img/24b944ae9ea7407934ac4f712a52ac9e.png">的特征向量是

A. <img src="https://tihai-oss-cloud.itihey.com/img/e413222b276bdaaf3d7aea90177c9dda.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/95b902326ac3ed6fef555cf9ea461b74.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/54a4a8cfe4c4dec01e8df0028261abf2.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/34051f118e2d67bc647bb9b3c151acac.png">

下列说法正确的有

A. 非零特征向量的特征值也是非零的B. 属于一个特征值的特征向量只能有一个C. 一个特征向量只能属于一个特征值D. n阶可逆矩阵有n个不同的特征值

设<img src="https://tihai-oss-cloud.itihey.com/img/945763c82dcedcd2dcac9f7588778cd4.gif">是三阶矩阵,且<img src="https://tihai-oss-cloud.itihey.com/img/9ea36ec7c496f5b5ef73d195d4bcb821.gif">均不可逆,<img src="https://tihai-oss-cloud.itihey.com/img/6b2fd3475afd4025bc1698f72578a797.gif">是<img src="https://tihai-oss-cloud.itihey.com/img/945763c82dcedcd2dcac9f7588778cd4.gif">的伴随矩阵,则行列式<img src="https://tihai-oss-cloud.itihey.com/img/098d0fcb95adb828c206b30a541993f5.gif">( )

A. 9/2B. -9/2C. 9/8D. -9/8

<img src="https://tihai-oss-cloud.itihey.com/img/2993950dce11fcbc262b345372744926.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/10a26b2038faaec25523361c4d8aeb58.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/b3c4f63357e908f2e311babe4e7a0042.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b750f59ddd4303693e38050a020c4863.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/01597882f3a0d9532edd8963ace04591.png">

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